According to The Times, Carter is planning to leave after the publication of the Digital Britain report next month.
The paper said Carter has told Brown he was looking to make a "low key" exit over the summer recess.
Carter denied he had a job lined up but refused to confirm whether he would still be a minister by the autumn.
There is speculation Carter could be in the running to replace ITV chief executive Michael Grade.
One barrier to his appointment could come in the form of the Advisory Committee on Business Appointments, which ensures ex-ministers entering the private sector do not hold trade sensitive information on competitors.
Eighteen months ago Carter was brought into 10 Downing Street from the PR agency Brunswick where he was chief executive.
His brief was to revitalise government communications after the prime minister was widely criticised for backing down from announcing a general election.
Carter's arrival at Number 10 ruffled a number of feathers, including those of chief spokesman Damien McBride, and sparked the exit of long-term advisers, including speechwriter Spencer Livermore.
There was also consternation that Carter was earning as much as Brown with his £180,000 a year package, not including perks.
Finally in September last year Carter, after 10 months in the job, from the role to be given a peerage and the role of communications minister.
Since then he has been the principal architect behind the report into how the UK accesses digital communications.
In an interim report in February, Carter laid out plans to put broadband into every home.
This week he became one of the Department of Business, Innovation and Skills ministers answering to Lord Mandleson, following last week's cabinet reshuffle.
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